Phase transitions and critical indices of a phospholipid bilayer model

A model is described which has been used in theoretical studies of a variety of phenomena (which are briefly summarized) relating to biological membranes. It is shown that the Hamiltonian describing this model can be mapped onto an Ising Hamiltonian with a temperature dependent field. It is also shown that this field varies linearly with temperature in the critical region. Exact solutions of this model are presented and its first and second order transitions are discussed with an emphasis on obtaining its critical indices. General considerations lead to the following relations: =1/, =, =, where , , , are the critical indices for the specific heat, magnetization, susceptibility and critical isotherm respectively (the primes denoting low temperature indices). These relations are demonstrated explicitly for the Bethe lattice with coordination numbersq=2 and 6.     

Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Constraints,phase transitions and critical indices

The notion of first order phase transitions is examined for systems under external constraints. It is emphasized that only discontinuities with respect to “natural” variables (additive extensive variables and their conjugate internal forces) should be regarded as first order transitions. The Baker-Essam model is accordingly reviewed, and it is shown that the transition is always of the second order. Fisher's conjecture about renormalization is shown to be correct also for this model.     

Phase transitions of bilayer spin-1/2 Baxter-Wu model with repulsive interlayer interactions

Using a Monte Carlo simulation and the single histogram reweighting technique, we study the critical behaviors and phase transitions of the Baxter-Wu model on a two-layer triangular lattice with repulsive interlayer interactions. Via the finite-size analysis, we obtain the transition temperatures and critical exponents at different interlayer coupling strengths. The reduced energy cumulants and the histograms reveal pseudo-first-order phase transitions, and the critical exponents derivate from the standard Baxter-Wu model if the coupling is weak. As the increase of the coupling, the behavior of the pseudo-first order transition disappears and the critical exponents are in accordance with the ones known for the 2D 4-state Potts model.     

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Phase transitions in a probabilistic cellular automaton: Growth kinetics and critical properties

We investigate a discrete-time kinetic model without detailed balance which simulates the phase segregation of a quenched binary alloy. The model is a variation on the Rothman-Keller cellular automaton in which particles of type A (B) move toward domains of greater concentration of A (B). Modifications include a fully occupied lattice and the introduction of a temperature-like parameter which endows the system with a stochastic evolution. Using computer simulations, we examine domain growth kinetics in the two-dimensional model. For long times after a quench from disorder, we find that the average domain sizeR(t) t ^1/3, in agreement with the prediction of Lifshitz-Slyozov-Wagner theory. Using a variety of methods, we analyze the critical properties of the associated second-order transition. Our analysis indicates that this model does not fall within either the Ising or mean-field classes.     

Phase transitions in the Ashkin-Teller model

For some values of the coupling constants, a proof of the existence of two phase transitions in the Ashkin-Teller model is given. Only correlation inequalities are used.     

一种新交通流跟驰模型的相变研究

本文通过数值仿真的方法研究了优化速度跟驰模型(OVM)描述由一辆预先给定速度曲线的头车运动而引起的车辆队列加速过程的性能，结果显示该模型在描述这一过程时具有某种缺陷。据此文章提出了一个新的模型，能够改进OVM的这一不足。对改进模型的线性稳定性分析表明：若稳定性条件不能满足，则随着初始均衡交通流车头间距的变化将会产生交通流的相变现象。     

Towards a microscopic theory of phase transitions: residual rays,correlation radii and critical indices

Bonds between atoms/molecules of condensed substances must be described within the framework of quantum electrodynamics (QED) as an exchange of virtual photons. Such representation is supported by the known conformity of latent heat with residual infrared (IR) rays and the possibility of latent heat removal by characteristic frequencies. These bonds are virtual if the duration of photons’ formation (their ‘dressing’) τ exceeds the duration of free path in substance ??=?1/σ _tot N, i.e. if τ?>??/c. It is assumed that reversing this inequality corresponds to bond breakage and phase transitions. With low σ _tot and τ frequencies, it leads to the universal radius of correlations, R _c?～?ω ^?ν, ν?=?2/3, and allows refinement of the Ginzburg–Landau model of phase transitions by expansion of thermodynamic potentials over R _c (instead of temperature distance), which results in the correct system of critical indices. Such a consideration offers an opportunity for the stimulation of definite phase transitions by resonant frequencies.     

Phase transitions and hysteresis in a cellular automata-based model of opinion formation

A particular case of a cellular automata-based model of two-state opinion formation in social groups with a strong leader is studied. We consider a 2D Euclidian geometry of social space and mutual interactions 1/r ⁿ . The model shows an interesting dynamics which can be analytically calculated. There are two stable states of the system: a cluster around the leader and unification. Unstable clusters may also appear. A variation in parameters such as the leader's strength or the social temperature can change the size of a cluster or, when they reach some critical values, make the system jump into another state. For a certain range of parameters the system exhibits bistability and hysteresis phenomena. We obtained explicit formulas for the cluster size, critical leader's strength, and critical social temperature. These analytical results are verified by computer simulations.     

Phase transitions in the mixed Ashkin-Teller model

By using a mean-field approximation (MFA) and Monte-Carlo (MC) simulations, we have studied the effect on the phase diagrams of mixed spins ( and S =1) in the Ashkin-Teller model (ATM) on a hypercubic lattice. By varying the strength describing the four spin interaction and the single ion potential, we have obtained by these two methods quite rich phase diagrams with several multicritical points. This model exhibits a new partially ordered phase which does not exist neither in the spin-1/2 ATM nor in the spin-1 ATM. While MFA yields phase diagrams which are sometimes qualitatively incorrect, accurate results are obtained from MC simulations. From the critical exponents which have been calculated using finite-size scaling ideas, we have shown that all phase transitions are Ising-like except for the paramagnetic-Baxter critical surface on which the critical exponents vary continuously, by varying only the strength of the coupling interaction independently of the value of the single ion potential. Received 5 July 1999 and Received in final form 4 July 2000     

Phase transitions in three-dimensional three-state Potts model

We have performed a Monte Carlo investigation of the nature of the phase transition in the three-state, three-dimensional Potts model with nearest and next nearest neighbour coupling. We find strong evidence for a first-order phase transition in the case of ferromagnetic coupling. In the case of a first neighbour ferromagnetic coupling and second neighbour antiferromagnetic, there is evidence for a second-order transition. This result supports the idea that a second-order transition can be present in systems which, according to the Landau criterium, should only undergo a first-order transition.     

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.     

Phase transitions in a fluid surface model with a deficit angle term

Nambu-Goto model is investigated by using the canonical Monte Carlo simulation technique on dynamically triangulated surfaces of spherical topology. We find that the model has four distinct phases; crumpled, branched-polymer, linear, and tubular. The linear phase and the tubular phase appear to be separated by a first-order transition. It is also found that there is no long-range two-dimensional order in the model. In fact, no smooth surface can be seen in the whole region of the curvature modulus α, which is the coefficient of the deficit angle term in the Hamiltonian. The bending energy, which is not included in the Hamiltonian, remains large even at sufficiently large α in the tubular phase. On the other hand, the surface is spontaneously compactified into a one-dimensional smooth curve in the linear phase; one of the two degrees of freedom shrinks, and the other degree of freedom remains along the curve. Moreover, we find that the rotational symmetry of the model is spontaneously broken in the tubular phase just as in the same model on the fixed connectivity surfaces.